An idealized, though simplistic, view of the referring expression production and grounding process in (situated) dialogue assumes that a speaker must merely appropriately specify their expression so that the target referent may be successfully identified by the addressee. However, referring in conversation is a collaborative process that cannot be aptly characterized as an exchange of minimally-specified referring expressions. Concerns have been raised regarding assumptions made by prior work on visually-grounded dialogue that reveal an oversimplified view of conversation and the referential process. We address these concerns by introducing a collaborative image ranking task, a grounded agreement game we call “A Game Of Sorts”. In our game, players are tasked with reaching agreement on how to rank a set of images given some sorting criterion through a largely unrestricted, role-symmetric dialogue. By putting emphasis on the argumentation in this mixed-initiative interaction, we collect discussions that involve the collaborative referential process. We describe results of a small-scale data collection experiment with the proposed task. All discussed materials, which includes the collected data, the codebase, and a containerized version of the application, are publicly available.